Built with doc-gen4, running Lean4. Bubbles () indicate interactive fragments: hover for details, tap to reveal contents. Use Ctrl+↑Ctrl+↓to navigate, Ctrl+🖱️to focus. On Mac, use Cmdinstead of Ctrl.
import ECTate.Algebra.EllipticCurve.Kronecker
import ECTate.Algebra.EllipticCurve.Model
import ECTate.Algebra.ValuedRing
import ECTate.Data.Nat.Enat
import Mathlib.Data.Int.Basic
import Mathlib.Tactic.LibrarySearch
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Contrapose

open Enat

variable {
R: Type u
R
:
Type u: Type (u + 1)
Type u
} [inst :
IntegralDomain: Type ?u.19993Type ?u.19993
IntegralDomain
R: Type u
R
] namespace Model variable {
p: R
p
:
R: Type u
R
} def
is_local_singular_point: {R : Type u} → [inst : IntegralDomain R] → {p : R} → SurjVal pModel RR × RProp
is_local_singular_point
(
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.21} → R[inst : IntegralDomain R] → Type ?u.21
SurjVal
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.30) → [inst : IntegralDomain R] → Type ?u.30
Model
R: Type u
R
) (
P: R × R
P
:
R: Type u
R
×
R: Type u
R
) :
Prop: Type
Prop
:=
valp: SurjVal p
valp
.
v: {R : Type ?u.43} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
weierstrass: {R : Type ?u.50} → [inst : IntegralDomain R] → Model RR × RR
weierstrass
e: Model R
e
P: R × R
P
) >
0: ?m.58
0
valp: SurjVal p
valp
.
v: {R : Type ?u.312} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
dweierstrass_dx: {R : Type ?u.316} → [inst : IntegralDomain R] → Model RR × RR
dweierstrass_dx
e: Model R
e
P: R × R
P
) >
0: ?m.320
0
valp: SurjVal p
valp
.
v: {R : Type ?u.338} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
dweierstrass_dy: {R : Type ?u.342} → [inst : IntegralDomain R] → Model RR × RR
dweierstrass_dy
e: Model R
e
P: R × R
P
) >
0: ?m.346
0
lemma
Warning: declaration uses 'sorry'
(
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.383} → R[inst : IntegralDomain R] → Type ?u.383
SurjVal
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.392) → [inst : IntegralDomain R] → Type ?u.392
Model
R: Type u
R
) (
h: SurjVal.v valp (discr e) > 0
h
:
valp: SurjVal p
valp
.
v: {R : Type ?u.397} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
discr: {R : Type ?u.404} → [inst : IntegralDomain R] → Model RR
discr
>
0: ?m.413
0
) : ∃
P: ?m.671
P
,
is_local_singular_point: {R : Type ?u.673} → [inst : IntegralDomain R] → {p : R} → SurjVal pModel RR × RProp
is_local_singular_point
valp: SurjVal p
valp
e: Model R
e
P: ?m.671
P
:=
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: Model R

h: SurjVal.v valp (discr e) > 0


P, is_local_singular_point valp e P

Goals accomplished! 🐙
def
move_singular_point_to_origin_triple: {R : Type u} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RR × R × R
move_singular_point_to_origin_triple
(evr :
EnatValRing: {R : Type ?u.707} → R[inst : IntegralDomain R] → Type ?u.707
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.716) → [inst : IntegralDomain R] → Type ?u.716
Model
R: Type u
R
) :
R: Type u
R
×
R: Type u
R
×
R: Type u
R
:= match evr.
residue_char: {R : Type ?u.734} → {p : R} → [inst : IntegralDomain R] → EnatValRing p
residue_char
with |
2:
2
=> (evr.
norm_repr: {R : Type ?u.758} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
e: Model R
e
.
a4: {R : Type ?u.762} → [inst : IntegralDomain R] → Model RR
a4
,
0: ?m.772
0
, evr.
norm_repr: {R : Type ?u.835} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(
e: Model R
e
.
a6: {R : Type ?u.842} → [inst : IntegralDomain R] → Model RR
a6
+
e: Model R
e
.
a4: {R : Type ?u.848} → [inst : IntegralDomain R] → Model RR
a4
*
e: Model R
e
.
a2: {R : Type ?u.851} → [inst : IntegralDomain R] → Model RR
a2
)) |
3:
3
=> (evr.
norm_repr: {R : Type ?u.1074} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(-
e: Model R
e
.
b6: {R : Type ?u.1079} → [inst : IntegralDomain R] → Model RR
b6
),
0: ?m.1118
0
, evr.
norm_repr: {R : Type ?u.1120} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(
e: Model R
e
.
a3: {R : Type ?u.1127} → [inst : IntegralDomain R] → Model RR
a3
-
e: Model R
e
.
b6: {R : Type ?u.1133} → [inst : IntegralDomain R] → Model RR
b6
*
e: Model R
e
.
a1: {R : Type ?u.1139} → [inst : IntegralDomain R] → Model RR
a1
)) | _ => (
0: ?m.1279
0
,
0: ?m.1286
0
,
0: ?m.1289
0
) --need to fill here def
move_singular_point_to_origin_iso: {R : Type u} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
move_singular_point_to_origin_iso
(evr :
EnatValRing: {R : Type ?u.2056} → R[inst : IntegralDomain R] → Type ?u.2056
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.2065) → [inst : IntegralDomain R] → Type ?u.2065
Model
R: Type u
R
) :
Model: (R : Type ?u.2069) → [inst : IntegralDomain R] → Type ?u.2069
Model
R: Type u
R
:=
rst_triple: {R : Type ?u.2074} → [inst : IntegralDomain R] → Model RR × R × RModel R
rst_triple
e: Model R
e
(
move_singular_point_to_origin_triple: {R : Type ?u.2079} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RR × R × R
move_singular_point_to_origin_triple
evr
e: Model R
e
) lemma
Warning: declaration uses 'sorry'
(evr :
EnatValRing: {R : Type ?u.2166} → R[inst : IntegralDomain R] → Type ?u.2166
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.2171) → [inst : IntegralDomain R] → Type ?u.2171
Model
R: Type u
R
) : (∃
P: ?m.2179
P
,
is_local_singular_point: {R : Type ?u.2181} → [inst : IntegralDomain R] → {p : R} → SurjVal pModel RR × RProp
is_local_singular_point
valp: ?m.2163
valp
e: Model R
e
P: ?m.2179
P
) →
is_local_singular_point: {R : Type ?u.2200} → [inst : IntegralDomain R] → {p : R} → SurjVal pModel RR × RProp
is_local_singular_point
valp: ?m.2163
valp
(
move_singular_point_to_origin_iso: {R : Type ?u.2210} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
move_singular_point_to_origin_iso
evr
e: Model R
e
) (
0: ?m.2222
0
,
0: ?m.2286
0
) :=
R: Type u

inst: IntegralDomain R

p, p✝: R

valp: SurjVal p✝

evr: EnatValRing p

e: Model R



Goals accomplished! 🐙
def
pi_scaling: {R : Type u} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
(evr :
EnatValRing: {R : Type ?u.2324} → R[inst : IntegralDomain R] → Type ?u.2324
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.2333) → [inst : IntegralDomain R] → Type ?u.2333
Model
R: Type u
R
) :
Model: (R : Type ?u.2337) → [inst : IntegralDomain R] → Type ?u.2337
Model
R: Type u
R
:= { a1 := evr.
sub_val: {R : Type ?u.2347} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.2360} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.2364
1
, a2 := evr.
sub_val: {R : Type ?u.2374} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a2: {R : Type ?u.2384} → [inst : IntegralDomain R] → Model RR
a2
2: ?m.2388
2
, a3 := evr.
sub_val: {R : Type ?u.2393} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.2403} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.2407
3
, a4 := evr.
sub_val: {R : Type ?u.2412} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.2422} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.2426
4
, a6 := evr.
sub_val: {R : Type ?u.2431} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a6: {R : Type ?u.2441} → [inst : IntegralDomain R] → Model RR
a6
6: ?m.2445
6
} lemma
pi_scaling_of_b2: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2
pi_scaling_of_b2
(evr :
EnatValRing: {R : Type ?u.2530} → R[inst : IntegralDomain R] → Type ?u.2530
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.2539) → [inst : IntegralDomain R] → Type ?u.2539
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.2544} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.2551} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.2558} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.2564
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.2582} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.2586} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.2590} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.2594
2
) : evr.
sub_val: {R : Type ?u.2604} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.2614} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.2621
2
= evr.
sub_val: {R : Type ?u.2629} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.2639} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.2643
1
* evr.
sub_val: {R : Type ?u.2645} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.2655} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.2659
1
+
4: ?m.2665
4
* evr.
sub_val: {R : Type ?u.2674} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a2: {R : Type ?u.2684} → [inst : IntegralDomain R] → Model RR
a2
2: ?m.2688
2
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a1) 1 + 4 * EnatValRing.sub_val evr e.a2 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1) 1) 1 + 4 * EnatValRing.sub_val evr e.a2 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) + 4 * EnatValRing.sub_val evr e.a2 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) + EnatValRing.sub_val evr (4 * e.a2) 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)

Goals accomplished! 🐙
lemma
pi_scaling_of_b4: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4
pi_scaling_of_b4
(evr :
EnatValRing: {R : Type ?u.3323} → R[inst : IntegralDomain R] → Type ?u.3323
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.3332) → [inst : IntegralDomain R] → Type ?u.3332
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.3337} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.3344} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.3351} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.3357
1
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.3375} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.3379} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.3383} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.3387
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.3397} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.3401} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.3405} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.3409
4
) : evr.
sub_val: {R : Type ?u.3419} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b4: {R : Type ?u.3429} → [inst : IntegralDomain R] → Model RR
b4
4: ?m.3436
4
= evr.
sub_val: {R : Type ?u.3444} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.3454} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.3458
1
* evr.
sub_val: {R : Type ?u.3460} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.3470} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.3474
3
+
2: ?m.3480
2
* evr.
sub_val: {R : Type ?u.3489} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.3499} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.3503
4
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a3) 3 + 2 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) 1) 3 + 2 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) + 2 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) + EnatValRing.sub_val evr (2 * e.a4) 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)

Goals accomplished! 🐙
lemma
pi_scaling_of_b6: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a6 ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6
pi_scaling_of_b6
(evr :
EnatValRing: {R : Type ?u.4140} → R[inst : IntegralDomain R] → Type ?u.4140
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.4149) → [inst : IntegralDomain R] → Type ?u.4149
Model
R: Type u
R
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.4154} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4161} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.4168} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.4174
3
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.4191} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4195} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.4199} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.4203
6
) : evr.
sub_val: {R : Type ?u.4213} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.4223} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.4230
6
= evr.
sub_val: {R : Type ?u.4238} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.4248} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.4252
3
* evr.
sub_val: {R : Type ?u.4254} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.4264} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.4268
3
+
4: ?m.4274
4
* evr.
sub_val: {R : Type ?u.4283} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a6: {R : Type ?u.4293} → [inst : IntegralDomain R] → Model RR
a6
6: ?m.4297
6
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a3 3 * e.a3) 3 + 4 * EnatValRing.sub_val evr e.a6 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a3 * e.a3) 3) 3 + 4 * EnatValRing.sub_val evr e.a6 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3) (3 + 3) + 4 * EnatValRing.sub_val evr e.a6 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3) (3 + 3) + EnatValRing.sub_val evr (4 * e.a6) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)

Goals accomplished! 🐙
lemma
pi_scaling_of_b8: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
pi_scaling_of_b8
(evr :
EnatValRing: {R : Type ?u.4932} → R[inst : IntegralDomain R] → Type ?u.4932
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.4941) → [inst : IntegralDomain R] → Type ?u.4941
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.4946} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4953} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.4960} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.4966
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.4984} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4988} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.4992} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.4996
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.5006} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.5010} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.5014} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.5018
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.5028} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.5032} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.5036} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.5040
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.5050} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.5054} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.5058} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.5062
6
) : evr.
sub_val: {R : Type ?u.5072} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b8: {R : Type ?u.5082} → [inst : IntegralDomain R] → Model RR
b8
8: ?m.5089
8
= evr.
sub_val: {R : Type ?u.5112} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.5122} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.5126
1
* evr.
sub_val: {R : Type ?u.5128} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.5138} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.5142
1
* evr.
sub_val: {R : Type ?u.5144} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a6: {R : Type ?u.5154} → [inst : IntegralDomain R] → Model RR
a6
6: ?m.5158
6
- evr.
sub_val: {R : Type ?u.5166} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.5176} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.5180
1
* evr.
sub_val: {R : Type ?u.5182} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.5192} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.5196
3
* evr.
sub_val: {R : Type ?u.5198} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.5208} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.5212
4
+
4: ?m.5221
4
* evr.
sub_val: {R : Type ?u.5230} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a2: {R : Type ?u.5240} → [inst : IntegralDomain R] → Model RR
a2
2: ?m.5244
2
* evr.
sub_val: {R : Type ?u.5246} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a6: {R : Type ?u.5256} → [inst : IntegralDomain R] → Model RR
a6
6: ?m.5260
6
+ evr.
sub_val: {R : Type ?u.5268} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a2: {R : Type ?u.5278} → [inst : IntegralDomain R] → Model RR
a2
2: ?m.5282
2
* evr.
sub_val: {R : Type ?u.5284} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.5294} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.5298
3
* evr.
sub_val: {R : Type ?u.5300} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.5310} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.5314
3
- evr.
sub_val: {R : Type ?u.5319} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.5329} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.5333
4
* evr.
sub_val: {R : Type ?u.5335} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.5345} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.5349
4
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) * e.a6) 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1)) 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a3) 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) 1) 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) * e.a4) 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3)) 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2) 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (4 * e.a2) 2 * e.a6) 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (4 * e.a2 * e.a6) 2) 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * EnatValRing.sub_val evr e.a3 3) 2 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * EnatValRing.sub_val evr e.a3 3) 2 * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3) 3) 2 * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3) (3 + 2) * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3)) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a4 4 * e.a4) 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a4 * e.a4) 4) 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 1 + ofN 3 + ofN 4


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 1 + ofN 3 + ofN 4

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 2 + ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 1 + ofN 3 + ofN 4

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 2 + ofN 6

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 2 + ofN 3 + ofN 3


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 1 + ofN 3 + ofN 4

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 2 + ofN 6

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 2 + ofN 3 + ofN 3

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN 4 + ofN 4


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + -EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + EnatValRing.sub_val evr (-(e.a1 * e.a3 * e.a4)) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + EnatValRing.sub_val evr (-(e.a1 * e.a3 * e.a4)) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) (1 + 1 + 6) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 + -(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)

Goals accomplished! 🐙
open EnatValRing in lemma
pi_scaling_of_discr: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn (b2 e) ofN 2SurjVal.v evr.valtn (b4 e) ofN 4SurjVal.v evr.valtn (b6 e) ofN 6SurjVal.v evr.valtn (b8 e) ofN 8sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
pi_scaling_of_discr
(evr :
EnatValRing: {R : Type ?u.8108} → R[inst : IntegralDomain R] → Type ?u.8108
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.8117) → [inst : IntegralDomain R] → Type ?u.8117
Model
R: Type u
R
) (
hb2: SurjVal.v evr.valtn (b2 e) ofN 2
hb2
: evr.
valtn: {R : Type ?u.8122} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.8129} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b2: {R : Type ?u.8136} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
2: ?m.8145
2
) (
hb4: SurjVal.v evr.valtn (b4 e) ofN 4
hb4
: evr.
valtn: {R : Type ?u.8162} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.8166} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b4: {R : Type ?u.8170} → [inst : IntegralDomain R] → Model RR
b4
ofN: ℕ∪∞
ofN
4: ?m.8177
4
) (
hb6: SurjVal.v evr.valtn (b6 e) ofN 6
hb6
: evr.
valtn: {R : Type ?u.8187} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.8191} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b6: {R : Type ?u.8195} → [inst : IntegralDomain R] → Model RR
b6
ofN: ℕ∪∞
ofN
6: ?m.8202
6
) (
hb8: SurjVal.v evr.valtn (b8 e) ofN 8
hb8
: evr.
valtn: {R : Type ?u.8212} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.8216} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b8: {R : Type ?u.8220} → [inst : IntegralDomain R] → Model RR
b8
ofN: ℕ∪∞
ofN
8: ?m.8227
8
) : evr.
sub_val: {R : Type ?u.8237} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
discr: {R : Type ?u.8247} → [inst : IntegralDomain R] → Model RR
discr
12: ?m.8254
12
= -evr.
sub_val: {R : Type ?u.8275} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.8285} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.8292
2
* evr.
sub_val: {R : Type ?u.8294} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.8304} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.8311
2
* evr.
sub_val: {R : Type ?u.8313} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b8: {R : Type ?u.8323} → [inst : IntegralDomain R] → Model RR
b8
8: ?m.8330
8
-
8: ?m.8336
8
* ((evr.
sub_val: {R : Type ?u.8348} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b4: {R : Type ?u.8358} → [inst : IntegralDomain R] → Model RR
b4
4: ?m.8365
4
) ^
3: ?m.8368
3
) -
27: ?m.8384
27
* evr.
sub_val: {R : Type ?u.8393} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.8403} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.8410
6
* evr.
sub_val: {R : Type ?u.8412} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.8422} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.8429
6
+
9: ?m.8441
9
* evr.
sub_val: {R : Type ?u.8450} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.8460} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.8467
2
* evr.
sub_val: {R : Type ?u.8469} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b4: {R : Type ?u.8479} → [inst : IntegralDomain R] → Model RR
b4
4: ?m.8486
4
* evr.
sub_val: {R : Type ?u.8488} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.8498} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.8505
6
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e * b8 e) 12 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e) 4 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e) 6 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


-sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2

Goals accomplished! 🐙

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2

Goals accomplished! 🐙

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2

Goals accomplished! 🐙

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.hb
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
lemma
b2_of_pi_scaling: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2b2 (pi_scaling evr e) = EnatValRing.sub_val evr (b2 e) 2
b2_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.12841} → R[inst : IntegralDomain R] → Type ?u.12841
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.12850) → [inst : IntegralDomain R] → Type ?u.12850
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.12855} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12862} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.12869} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.12875
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.12893} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12897} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.12901} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.12905
2
) : (
pi_scaling: {R : Type ?u.12915} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
b2: {R : Type ?u.12922} → [inst : IntegralDomain R] → Model RR
b2
= evr.
sub_val: {R : Type ?u.12928} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.12938} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.12945
2
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2



Goals accomplished! 🐙
lemma
b4_of_pi_scaling: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4b4 (pi_scaling evr e) = EnatValRing.sub_val evr (b4 e) 4
b4_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.13210} → R[inst : IntegralDomain R] → Type ?u.13210
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.13219) → [inst : IntegralDomain R] → Type ?u.13219
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.13224} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13231} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.13238} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.13244
1
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.13262} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13266} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.13270} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.13274
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.13284} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13288} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.13292} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.13296
4
) : (
pi_scaling: {R : Type ?u.13306} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
b4: {R : Type ?u.13313} → [inst : IntegralDomain R] → Model RR
b4
= evr.
sub_val: {R : Type ?u.13319} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b4: {R : Type ?u.13329} → [inst : IntegralDomain R] → Model RR
b4
4: ?m.13336
4
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4



Goals accomplished! 🐙
lemma
b6_of_pi_scaling: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a6 ofN 6b6 (pi_scaling evr e) = EnatValRing.sub_val evr (b6 e) 6
b6_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.13603} → R[inst : IntegralDomain R] → Type ?u.13603
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.13612) → [inst : IntegralDomain R] → Type ?u.13612
Model
R: Type u
R
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.13617} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13624} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.13631} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.13637
3
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.13654} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13658} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.13662} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.13666
6
) : (
pi_scaling: {R : Type ?u.13676} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
b6: {R : Type ?u.13683} → [inst : IntegralDomain R] → Model RR
b6
= evr.
sub_val: {R : Type ?u.13689} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.13699} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.13706
6
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6



Goals accomplished! 🐙
lemma
b8_of_pi_scaling: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6b8 (pi_scaling evr e) = EnatValRing.sub_val evr (b8 e) 8
b8_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.13971} → R[inst : IntegralDomain R] → Type ?u.13971
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.13980) → [inst : IntegralDomain R] → Type ?u.13980
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.13985} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13992} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.13999} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.14005
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.14023} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14027} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.14031} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.14035
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.14045} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14049} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.14053} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.14057
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.14067} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14071} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.14075} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.14079
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.14089} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14093} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.14097} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.14101
6
) : (
pi_scaling: {R : Type ?u.14111} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
b8: {R : Type ?u.14118} → [inst : IntegralDomain R] → Model RR
b8
= evr.
sub_val: {R : Type ?u.14124} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b8: {R : Type ?u.14134} → [inst : IntegralDomain R] → Model RR
b8
8: ?m.14141
8
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6



Goals accomplished! 🐙
lemma
val_b2_of_val_a12: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn (b2 e) ofN 2
val_b2_of_val_a12
(evr :
EnatValRing: {R : Type ?u.14447} → R[inst : IntegralDomain R] → Type ?u.14447
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.14456) → [inst : IntegralDomain R] → Type ?u.14456
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.14461} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14468} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.14475} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.14481
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.14499} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14503} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.14507} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.14511
2
) : evr.
valtn: {R : Type ?u.14521} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14525} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b2: {R : Type ?u.14529} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
2: ?m.14536
2
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1 + 4 * e.a2) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


ha
SurjVal.v evr.valtn (e.a1 * e.a1) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


hb
SurjVal.v evr.valtn (4 * e.a2) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


ha
SurjVal.v evr.valtn (e.a1 * e.a1) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


ha
SurjVal.v evr.valtn (e.a1 * e.a1) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


hb
SurjVal.v evr.valtn (4 * e.a2) ofN 2

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


hb
SurjVal.v evr.valtn (4 * e.a2) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


hb
SurjVal.v evr.valtn (4 * e.a2) ofN 2

Goals accomplished! 🐙
lemma
val_b4_of_val_a134: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn (b4 e) ofN 4
val_b4_of_val_a134
(evr :
EnatValRing: {R : Type ?u.14816} → R[inst : IntegralDomain R] → Type ?u.14816
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.14825) → [inst : IntegralDomain R] → Type ?u.14825
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.14830} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14837} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.14844} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.14850
1
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.14868} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14872} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.14876} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.14880
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.14890} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14894} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.14898} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.14902
4
) : evr.
valtn: {R : Type ?u.14912} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14916} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b4: {R : Type ?u.14920} → [inst : IntegralDomain R] → Model RR
b4
ofN: ℕ∪∞
ofN
4: ?m.14927
4
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (b4 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3 + 2 * e.a4) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (b4 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


ha
SurjVal.v evr.valtn (e.a1 * e.a3) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


hb
SurjVal.v evr.valtn (2 * e.a4) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (b4 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


ha
SurjVal.v evr.valtn (e.a1 * e.a3) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


ha
SurjVal.v evr.valtn (e.a1 * e.a3) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


hb
SurjVal.v evr.valtn (2 * e.a4) ofN 4

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (b4 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


hb
SurjVal.v evr.valtn (2 * e.a4) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


hb
SurjVal.v evr.valtn (2 * e.a4) ofN 4

Goals accomplished! 🐙
lemma
val_b6_of_val_a36: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a6 ofN 6SurjVal.v evr.valtn (b6 e) ofN 6
val_b6_of_val_a36
(evr :
EnatValRing: {R : Type ?u.15216} → R[inst : IntegralDomain R] → Type ?u.15216
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.15225) → [inst : IntegralDomain R] → Type ?u.15225
Model
R: Type u
R
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.15230} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15237} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.15244} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.15250
3
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.15267} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15271} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.15275} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.15279
6
) : evr.
valtn: {R : Type ?u.15289} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15293} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b6: {R : Type ?u.15297} → [inst : IntegralDomain R] → Model RR
b6
ofN: ℕ∪∞
ofN
6: ?m.15304
6
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3 + 4 * e.a6) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a3 * e.a3) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (4 * e.a6) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a3 * e.a3) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a3 * e.a3) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (4 * e.a6) ofN 6

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (4 * e.a6) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (4 * e.a6) ofN 6

Goals accomplished! 🐙
lemma
val_b8_of_val_ai: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6SurjVal.v evr.valtn (b8 e) ofN 8
val_b8_of_val_ai
(evr :
EnatValRing: {R : Type ?u.15584} → R[inst : IntegralDomain R] → Type ?u.15584
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.15593) → [inst : IntegralDomain R] → Type ?u.15593
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.15598} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15605} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.15612} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.15618
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.15636} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15640} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.15644} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.15648
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.15658} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15662} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.15666} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.15670
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.15680} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15684} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.15688} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.15692
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.15702} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15706} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.15710} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.15714
6
) : evr.
valtn: {R : Type ?u.15724} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15728} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b8: {R : Type ?u.15732} → [inst : IntegralDomain R] → Model RR
b8
ofN: ℕ∪∞
ofN
8: ?m.15739
8
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b8 e) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 + -(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b8 e) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b8 e) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * (e.a2 * e.a6)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * (e.a2 * e.a6)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b8 e) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (e.a4 * e.a4) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (e.a4 * e.a4) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8

Goals accomplished! 🐙
lemma
discr_of_pi_scaling: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6discr (pi_scaling evr e) = EnatValRing.sub_val evr (discr e) 12
discr_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.16634} → R[inst : IntegralDomain R] → Type ?u.16634
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.16643) → [inst : IntegralDomain R] → Type ?u.16643
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.16648} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16655} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.16662} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.16668
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.16686} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16690} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.16694} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.16698
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.16708} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16712} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.16716} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.16720
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.16730} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16734} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.16738} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.16742
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.16752} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16756} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.16760} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.16764
6
) : (
pi_scaling: {R : Type ?u.16774} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
discr: {R : Type ?u.16781} → [inst : IntegralDomain R] → Model RR
discr
= evr.
sub_val: {R : Type ?u.16787} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
discr: {R : Type ?u.16797} → [inst : IntegralDomain R] → Model RR
discr
12: ?m.16804
12
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


-EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b8 e) 8 - 8 * EnatValRing.sub_val evr (b4 e) 4 ^ 3 - 27 * EnatValRing.sub_val evr (b6 e) 6 * EnatValRing.sub_val evr (b6 e) 6 + 9 * EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b4 e) 4 * EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e) 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6



Goals accomplished! 🐙
lemma
val_discr_of_val_ai: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6SurjVal.v evr.valtn (discr e) ofN 12
val_discr_of_val_ai
(evr :
EnatValRing: {R : Type ?u.17281} → R[inst : IntegralDomain R] → Type ?u.17281
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.17290) → [inst : IntegralDomain R] → Type ?u.17290
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.17295} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.17302} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.17309} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.17315
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.17333} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.17337} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.17341} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.17345
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.17355} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.17359} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.17363} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.17367
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.17377} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.17381} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.17385} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.17389
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.17399} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.17403} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.17407} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.17411
6
) : evr.
valtn: {R : Type ?u.17421} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.17425} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
discr: {R : Type ?u.17429} → [inst : IntegralDomain R] → Model RR
discr
ofN: ℕ∪∞
ofN
12: ?m.17436
12
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e) + 9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-(b2 e * b2 e) * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-(b2 e * b2 e * b8 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * (b4 e ^ 2 * b4 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * (b4 e ^ 1 * b4 e * b4 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * (b4 e * b4 e * b4 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * (b4 e * b4 e * b4 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (27 * (b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (27 * (b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * (b4 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * (b2 e * (b4 e * b6 e))) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * (b2 e * (b4 e * b6 e))) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
end Model namespace ValidModel def
pi_scaling: {p : R} → (evr : EnatValRing p) → (e : ValidModel R) → SurjVal.v evr.valtn e.toModel.a1 ofN 1SurjVal.v evr.valtn e.toModel.a2 ofN 2SurjVal.v evr.valtn e.toModel.a3 ofN 3SurjVal.v evr.valtn e.toModel.a4 ofN 4SurjVal.v evr.valtn e.toModel.a6 ofN 6ValidModel R
pi_scaling
(evr :
EnatValRing: {R : Type ?u.19032} → R[inst : IntegralDomain R] → Type ?u.19032
EnatValRing
p: ?m.19029
p
) (e :
ValidModel: (R : Type ?u.19040) → [inst : IntegralDomain R] → Type ?u.19040
ValidModel
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.19049} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19062} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.19077} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.19083
1
) (
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.19101} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19108} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.19118} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.19122
2
) (
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.19132} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19136} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.19143} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.19147
3
) (
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.19157} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19161} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.19168} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.19172
4
) (
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.19182} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19186} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.19193} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.19197
6
) :
ValidModel: (R : Type ?u.19206) → [inst : IntegralDomain R] → Type ?u.19206
ValidModel
R: Type u
R
:= { toModel :=
Model.pi_scaling: {R : Type ?u.19220} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
Model.pi_scaling
evr e.
toModel: {R : Type ?u.19224} → [inst : IntegralDomain R] → ValidModel RModel R
toModel
, discr_not_zero :=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


EnatValRing.sub_val evr (Model.discr e.toModel) 12 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


EnatValRing.sub_val evr (Model.discr e.toModel) 12 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': (let x := EnatValRing.sub_val evr (Model.discr e.toModel) 12; (fun x => p ^ 12 * x) x) = let x := 0; (fun x => p ^ 12 * x) x


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': p ^ 12 * EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': p ^ 12 * EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': Model.discr e.toModel = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': Model.discr e.toModel = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': Model.discr e.toModel = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0

Goals accomplished! 🐙
} lemma
toModel_pi_scaling: ∀ {p : R} (evr : EnatValRing p) (e : ValidModel R) (h1 : SurjVal.v evr.valtn e.toModel.a1 ofN 1) (h2 : SurjVal.v evr.valtn e.toModel.a2 ofN 2) (h3 : SurjVal.v evr.valtn e.toModel.a3 ofN 3) (h4 : SurjVal.v evr.valtn e.toModel.a4 ofN 4) (h6 : SurjVal.v evr.valtn e.toModel.a6 ofN 6), (pi_scaling evr e h1 h2 h3 h4 h6).toModel = Model.pi_scaling evr e.toModel
toModel_pi_scaling
(evr :
EnatValRing: {R : Type ?u.20002} → R[inst : IntegralDomain R] → Type ?u.20002
EnatValRing
p: ?m.19999
p
) (e :
ValidModel: (R : Type ?u.20010) → [inst : IntegralDomain R] → Type ?u.20010
ValidModel
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.20019} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20032} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.20047} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.20053
1
) (
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.20071} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20078} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.20088} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.20092
2
) (
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.20102} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20106} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.20113} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.20117
3
) (
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.20127} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20131} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.20138} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.20142
4
) (
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.20152} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20156} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.20163} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.20167
6
) : (e.
pi_scaling: {R : Type ?u.20177} → [inst : IntegralDomain R] → {p : R} → (evr : EnatValRing p) → (e : ValidModel R) → SurjVal.v evr.valtn e.toModel.a1 ofN 1SurjVal.v evr.valtn e.toModel.a2 ofN 2SurjVal.v evr.valtn e.toModel.a3 ofN 3SurjVal.v evr.valtn e.toModel.a4 ofN 4SurjVal.v evr.valtn e.toModel.a6 ofN 6ValidModel R
pi_scaling
evr
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
).
toModel: {R : Type ?u.20198} → [inst : IntegralDomain R] → ValidModel RModel R
toModel
= e.
toModel: {R : Type ?u.20201} → [inst : IntegralDomain R] → ValidModel RModel R
toModel
.
pi_scaling: {R : Type ?u.20204} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr :=
rfl: ∀ {α : Sort ?u.20226} {a : α}, a = a
rfl
def
val_discr_to_nat: {R : Type u} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.20418} → R[inst : IntegralDomain R] → Type ?u.20418
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.20427) → [inst : IntegralDomain R] → Type ?u.20427
ValidModel
R: Type u
R
) :
: Type
:=
nat_of_val: {R : Type ?u.20435} → [inst : IntegralDomain R] → {p : R} → SurjVal p{a : R} → a 0
nat_of_val
valp: SurjVal p
valp
e.
discr_not_zero: ∀ {R : Type ?u.20446} [inst : IntegralDomain R] (self : ValidModel R), Model.discr self.toModel 0
discr_not_zero
@[simp] lemma
iso_rst_val_discr_to_nat: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (valp : SurjVal p) (r s t : R) (e : ValidModel R), val_discr_to_nat valp (rst_iso r s t e) = val_discr_to_nat valp e
iso_rst_val_discr_to_nat
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.20507} → R[inst : IntegralDomain R] → Type ?u.20507
SurjVal
p: R
p
) (
r: R
r
s: R
s
t: R
t
:
R: Type u
R
) (e :
ValidModel: (R : Type ?u.20522) → [inst : IntegralDomain R] → Type ?u.20522
ValidModel
R: Type u
R
) :
val_discr_to_nat: {R : Type ?u.20527} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
valp: SurjVal p
valp
(
rst_iso: {R : Type ?u.20537} → [inst : IntegralDomain R] → RRRValidModel RValidModel R
rst_iso
r: R
r
s: R
s
t: R
t
e) =
val_discr_to_nat: {R : Type ?u.20542} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
valp: SurjVal p
valp
e :=
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

r, s, t: R

e: ValidModel R



Goals accomplished! 🐙
lemma
ofN_val_discr_to_nat: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (valp : SurjVal p) (e : ValidModel R), ofN (val_discr_to_nat valp e) = SurjVal.v valp (Model.discr e.toModel)
ofN_val_discr_to_nat
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.20944} → R[inst : IntegralDomain R] → Type ?u.20944
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.20953) → [inst : IntegralDomain R] → Type ?u.20953
ValidModel
R: Type u
R
) :
ofN: ℕ∪∞
ofN
(
val_discr_to_nat: {R : Type ?u.20958} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
valp: SurjVal p
valp
e) =
valp: SurjVal p
valp
.
v: {R : Type ?u.20970} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
discr: {R : Type ?u.20977} → [inst : IntegralDomain R] → Model RR
discr
:=
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R


ofN (val_discr_to_nat valp e) = SurjVal.v valp (Model.discr e.toModel)
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

x✝: ℕ∪∞

h: SurjVal.v valp (Model.discr e.toModel) = x✝


ofN (val_discr_to_nat valp e) = x✝
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
ofN (nat_of_val valp (_ : Model.discr e.toModel 0)) = ofN n
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
ofN (to_nat (_ : ¬SurjVal.v valp (Model.discr e.toModel) = )) = ofN n
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
SurjVal.v valp (Model.discr e.toModel) = ofN n
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
SurjVal.v valp (Model.discr e.toModel) = ofN n
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

x✝: ℕ∪∞

h: SurjVal.v valp (Model.discr e.toModel) = x✝


ofN (val_discr_to_nat valp e) = x✝
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: Model.discr e.toModel = 0


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: Model.discr e.toModel = 0


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: Model.discr e.toModel = 0


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top

Goals accomplished! 🐙
lemma
pi_scaling_val_discr_to_nat: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : ValidModel R) (h1 : SurjVal.v evr.valtn e.toModel.a1 ofN 1) (h2 : SurjVal.v evr.valtn e.toModel.a2 ofN 2) (h3 : SurjVal.v evr.valtn e.toModel.a3 ofN 3) (h4 : SurjVal.v evr.valtn e.toModel.a4 ofN 4) (h6 : SurjVal.v evr.valtn e.toModel.a6 ofN 6), val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
pi_scaling_val_discr_to_nat
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.21227} → R[inst : IntegralDomain R] → Type ?u.21227
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.21236) → [inst : IntegralDomain R] → Type ?u.21236
ValidModel
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.21241} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.21248} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.21260} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.21266
1
) (
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.21284} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.21288} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.21295} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.21299
2
) (
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.21309} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.21313} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.21320} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.21324
3
) (
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.21334} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.21338} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.21345} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.21349
4
) (
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.21359} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.21363} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.21370} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.21374
6
) :
val_discr_to_nat: {R : Type ?u.21384} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
evr.
valtn: {R : Type ?u.21388} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
(
pi_scaling: {R : Type ?u.21395} → [inst : IntegralDomain R] → {p : R} → (evr : EnatValRing p) → (e : ValidModel R) → SurjVal.v evr.valtn e.toModel.a1 ofN 1SurjVal.v evr.valtn e.toModel.a2 ofN 2SurjVal.v evr.valtn e.toModel.a3 ofN 3SurjVal.v evr.valtn e.toModel.a4 ofN 4SurjVal.v evr.valtn e.toModel.a6 ofN 6ValidModel R
pi_scaling
evr e
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
) =
val_discr_to_nat: {R : Type ?u.21406} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
evr.
valtn: {R : Type ?u.21410} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
e -
12: ?m.21418
12
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


ofN (val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6)) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


SurjVal.v evr.valtn (Model.discr (pi_scaling evr e h1 h2 h3 h4 h6).toModel) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


SurjVal.v evr.valtn (Model.discr (Model.pi_scaling evr e.toModel)) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


SurjVal.v evr.valtn (EnatValRing.sub_val evr (Model.discr e.toModel) 12) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


ofN (?m.21563 - 12) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


h
SurjVal.v evr.valtn (Model.discr e.toModel) = ofN ?m.21563
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


h
SurjVal.v evr.valtn (Model.discr e.toModel) = ofN (val_discr_to_nat evr.valtn e)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


h
SurjVal.v evr.valtn (Model.discr e.toModel) = ofN (val_discr_to_nat evr.valtn e)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


h
SurjVal.v evr.valtn (Model.discr e.toModel) = SurjVal.v evr.valtn (Model.discr e.toModel)

Goals accomplished! 🐙
lemma
v_b2_of_v_a1_a2: ∀ {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a1 ofN 1SurjVal.v valp e.toModel.a2 = ofN 1SurjVal.v valp (Model.b2 e.toModel) ofN 1
v_b2_of_v_a1_a2
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.21639} → R[inst : IntegralDomain R] → Type ?u.21639
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.21648) → [inst : IntegralDomain R] → Type ?u.21648
ValidModel
R: Type u
R
) (
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21653} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.21665} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.21671
1
) (
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h2
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21689} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.21696} → [inst : IntegralDomain R] → Model RR
a2
=
ofN: ℕ∪∞
ofN
1: ?m.21700
1
) :
valp: SurjVal p
valp
.
v: {R : Type ?u.21706} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b2: {R : Type ?u.21713} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
1: ?m.21720
1
:=
val_add_ge_of_ge: ∀ {R : Type ?u.21735} [inst : IntegralDomain R] {n : ℕ∪∞} {p : R} (nav : SurjVal p) {a b : R}, SurjVal.v nav a nSurjVal.v nav b nSurjVal.v nav (a + b) n
val_add_ge_of_ge
valp: SurjVal p
valp
(
val_mul_ge_of_left_ge: ∀ {R : Type ?u.21760} [inst : IntegralDomain R] {n : ℕ∪∞} {p : R} (nav : SurjVal p) {a b : R}, SurjVal.v nav a nSurjVal.v nav (a * b) n
val_mul_ge_of_left_ge
valp: SurjVal p
valp
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
) (
val_mul_ge_of_right_ge: ∀ {R : Type ?u.21776} [inst : IntegralDomain R] {n : ℕ∪∞} {p : R} (nav : SurjVal p) {a b : R}, SurjVal.v nav b nSurjVal.v nav (a * b) n
val_mul_ge_of_right_ge
valp: SurjVal p
valp
(
le_of_eq: ∀ {α : Type ?u.21786} [inst : Preorder α] {a b : α}, a = ba b
le_of_eq
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h2
.
symm: ∀ {α : Sort ?u.21797} {a b : α}, a = bb = a
symm
)) lemma
v_b4_of_v_a1_a3_a4: ∀ {R : Type u} [inst : IntegralDomain R] {q : } {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a1 ofN 1SurjVal.v valp e.toModel.a3 ofN qSurjVal.v valp e.toModel.a4 ofN (q + 1)SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)
v_b4_of_v_a1_a3_a4
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.21890} → R[inst : IntegralDomain R] → Type ?u.21890
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.21895) → [inst : IntegralDomain R] → Type ?u.21895
ValidModel
R: Type u
R
) (
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21900} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.21907} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.21911
1
) (
h3: SurjVal.v valp e.toModel.a3 ofN q
h3
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21918} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.21925} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
q: ?m.21885
q
) (
h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)
h4
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21933} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.21940} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
(
q: ?m.21885
q
+
1: ?m.21947
1
)) :
valp: SurjVal p
valp
.
v: {R : Type ?u.22004} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b4: {R : Type ?u.22011} → [inst : IntegralDomain R] → Model RR
b4
ofN: ℕ∪∞
ofN
(
q: ?m.21885
q
+
1: ?m.22021
1
) :=
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN q + ofN 1
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN 1 + ofN q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN 1 + ofN q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)

Goals accomplished! 🐙
lemma
v_b6_of_v_a3_a6: ∀ {q : } {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a3 ofN qSurjVal.v valp e.toModel.a6 ofN (2 * q)SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)
v_b6_of_v_a3_a6
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.22226} → R[inst : IntegralDomain R] → Type ?u.22226
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.22231) → [inst : IntegralDomain R] → Type ?u.22231
ValidModel
R: Type u
R
) (
h3: SurjVal.v valp e.toModel.a3 ofN q
h3
:
valp: SurjVal p
valp
.
v: {R : Type ?u.22236} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.22243} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
q: ?m.22221
q
) (
h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)
h6
:
valp: SurjVal p
valp
.
v: {R : Type ?u.22254} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.22261} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
(
2: ?m.22268
2
*
q: ?m.22221
q
)) :
valp: SurjVal p
valp
.
v: {R : Type ?u.22334} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b6: {R : Type ?u.22341} → [inst : IntegralDomain R] → Model RR
b6
ofN: ℕ∪∞
ofN
(
2: ?m.22351
2
*
q: ?m.22221
q
) :=
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (q + q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (q + q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)

Goals accomplished! 🐙
lemma
v_b8_of_v_ai: ∀ {q : } {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a1 ofN 1SurjVal.v valp e.toModel.a2 = ofN 1SurjVal.v valp e.toModel.a3 ofN qSurjVal.v valp e.toModel.a4 ofN (q + 1)SurjVal.v valp e.toModel.a6 ofN (2 * q)SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
v_b8_of_v_ai
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.22648} → R[inst : IntegralDomain R] → Type ?u.22648
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.22657) → [inst : IntegralDomain R] → Type ?u.22657
ValidModel
R: Type u
R
) (
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
:
valp: SurjVal p
valp
.
v: {R : Type ?u.22741} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.22748} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.22752
1
) (
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h2
:
valp: SurjVal p
valp
.
v: {R : Type ?u.22759} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.22766} → [inst : IntegralDomain R] → Model RR
a2
=
ofN: ℕ∪∞
ofN
1: ?m.22770
1
) (
h3: SurjVal.v valp e.toModel.a3 ofN q
h3
:
valp: SurjVal p
valp
.
v: {R : Type ?u.22776} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.22783} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
q: ?m.22726
q
) (
h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)
h4
:
valp: SurjVal p
valp
.
v: {R : Type ?u.22791} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.22798} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
(
q: ?m.22726
q
+
1: ?m.22805
1
)) (
h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)
h6
:
valp: SurjVal p
valp
.
v: {R : Type ?u.22862} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.22869} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
(
2: ?m.22876
2
*
q: ?m.22726
q
)) :
valp: SurjVal p
valp
.
v: {R : Type ?u.22938} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b8: {R : Type ?u.22945} → [inst : IntegralDomain R] → Model RR
b8
ofN: ℕ∪∞
ofN
(
2: ?m.22958
2
*
q: ?m.22726
q
+
1: ?m.22968
1
) :=
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 - e.toModel.a1 * e.toModel.a3 * e.toModel.a4 + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 - e.toModel.a4 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 - e.toModel.a1 * e.toModel.a3 * e.toModel.a4 + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 - e.toModel.a4 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 - e.toModel.a1 * e.toModel.a3 * e.toModel.a4 + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 + -(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 - e.toModel.a1 * e.toModel.a3 * e.toModel.a4 + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 - e.toModel.a4 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 + -(e.toModel.a1 * e.toModel.a3 * e.toModel.a4) + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 + -(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 + -(e.toModel.a1 * e.toModel.a3 * e.toModel.a4) + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 + -(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 + -(e.toModel.a1 * e.toModel.a3 * e.toModel.a4) + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 + -(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * (e.toModel.a1 * e.toModel.a6)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * (e.toModel.a1 * e.toModel.a6)) ofN (1 + 2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * (e.toModel.a1 * e.toModel.a6)) ofN 1 + ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * (e.toModel.a1 * e.toModel.a6)) ofN 1 + ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * e.toModel.a3 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN (q + q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN (q + (q + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN q + ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN q + ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * (e.toModel.a2 * e.toModel.a6)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * (e.toModel.a2 * e.toModel.a6)) ofN (1 + 2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * (e.toModel.a2 * e.toModel.a6)) ofN 1 + ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * (e.toModel.a2 * e.toModel.a6)) ofN 1 + ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN (q + q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN (1 + (q + q))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN 1 + ofN (q + q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN 1 + (ofN q + ofN q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN 1 + (ofN q + ofN q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN (q + q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN (q + (q + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN q + ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN q + ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
lemma
v_discr_of_v_ai: ∀ {q : } {p : R} (valp : SurjVal p) (e : ValidModel R), q > 1SurjVal.v valp e.toModel.a1 ofN 1SurjVal.v valp e.toModel.a2 = ofN 1SurjVal.v valp e.toModel.a3 ofN qSurjVal.v valp e.toModel.a4 ofN (q + 1)SurjVal.v valp e.toModel.a6 ofN (2 * q)SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
v_discr_of_v_ai
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.24442} → R[inst : IntegralDomain R] → Type ?u.24442
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.24431) → [inst : IntegralDomain R] → Type ?u.24431
ValidModel
R: Type u
R
) (
hq: q > 1
hq
:
q: ?m.24437
q
>
1: ?m.24453
1
) (
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
:
valp: SurjVal p
valp
.
v: {R : Type ?u.24490} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.24502} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.24508
1
) (
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h2
:
valp: SurjVal p
valp
.
v: {R : Type ?u.24526} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.24533} → [inst : IntegralDomain R] → Model RR
a2
=
ofN: ℕ∪∞
ofN
1: ?m.24537
1
) (
h3: SurjVal.v valp e.toModel.a3 ofN q
h3
:
valp: SurjVal p
valp
.
v: {R : Type ?u.24543} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.24550} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
q: ?m.24437
q
) (
h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)
h4
:
valp: SurjVal p
valp
.
v: {R : Type ?u.24558} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.24565} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
(
q: ?m.24437
q
+
1: ?m.24572
1
)) (
h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)
h6
:
valp: SurjVal p
valp
.
v: {R : Type ?u.24629} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.24636} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
(
2: ?m.24643
2
*
q: ?m.24437
q
)) :
valp: SurjVal p
valp
.
v: {R : Type ?u.24705} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
discr: {R : Type ?u.24712} → [inst : IntegralDomain R] → Model RR
discr
ofN: ℕ∪∞
ofN
(
2: ?m.24725
2
*
q: ?m.24437
q
+
3: ?m.24735
3
) :=
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel - 8 * Model.b4 e.toModel ^ 3 - 27 * Model.b6 e.toModel * Model.b6 e.toModel + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel - 8 * Model.b4 e.toModel ^ 3 - 27 * Model.b6 e.toModel * Model.b6 e.toModel + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel - 8 * Model.b4 e.toModel ^ 3 + -(27 * Model.b6 e.toModel * Model.b6 e.toModel) + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel - 8 * Model.b4 e.toModel ^ 3 - 27 * Model.b6 e.toModel * Model.b6 e.toModel + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel) + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel) + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-(Model.b2 e.toModel * Model.b2 e.toModel) * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-(Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + (1 + 1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + (1 + 1) + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 1 + 1 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 1 + (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b8 e.toModel * (Model.b2 e.toModel * Model.b2 e.toModel)) ofN (2 * q + 1 + (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b8 e.toModel * (Model.b2 e.toModel * Model.b2 e.toModel)) ofN (2 * q + 1) + ofN (1 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b8 e.toModel * (Model.b2 e.toModel * Model.b2 e.toModel)) ofN (2 * q + 1) + ofN (1 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * Model.b4 e.toModel ^ 3) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel ^ 2 * Model.b4 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel ^ 1 * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + 1 + (q + 1) + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + 1 + (q + 1)) + ofN 1
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + 1) + ofN (q + 1) + ofN 1
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + 1) + ofN (q + 1) + ofN 1
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * Model.b6 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * Model.b6 e.toModel * Model.b6 e.toModel) ofN (2 * q) + ofN 3
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * (Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q) + ofN 3
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * (Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q) + ofN 3

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * (Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q) + ofN (2 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * (Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q) + ofN (2 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


2 + 1 2 * q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


2 + 1 2 * q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


2 + 1 q + q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


2 + 1 q + q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + (1 + (1 + 1)))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q) + ofN (1 + (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q) + (ofN 1 + ofN (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (Model.b6 e.toModel * (9 * Model.b2 e.toModel * Model.b4 e.toModel)) ofN (2 * q) + (ofN 1 + ofN (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (Model.b6 e.toModel * (9 * (Model.b2 e.toModel * Model.b4 e.toModel))) ofN (2 * q) + (ofN 1 + ofN (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (Model.b6 e.toModel * (9 * (Model.b2 e.toModel * Model.b4 e.toModel))) ofN (2 * q) + (ofN 1 + ofN (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)

Goals accomplished! 🐙
lemma
small_char_div_12: ∀ {p : R}, p = 2 p = 3∀ (valp : SurjVal p), SurjVal.v valp 12 ofN 1
small_char_div_12
{
p: R
p
:
R: Type u
R
} (
hp: p = 2 p = 3
hp
:
p: R
p
=
2: ?m.28044
2
p: R
p
=
3: ?m.28122
3
) (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.28176} → R[inst : IntegralDomain R] → Type ?u.28176
SurjVal
p: R
p
) :
valp: SurjVal p
valp
.
v: {R : Type ?u.28184} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
12: ?m.28192
12
ofN: ℕ∪∞
ofN
1: ?m.28233
1
:=
R: Type u

inst: IntegralDomain R

p: R

hp: p = 2 p = 3

valp: SurjVal p


SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

hp: p = 2 p = 3

valp: SurjVal p


SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp (2 * 6) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp (2 * 6) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl.ha
SurjVal.v valp 2 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl.ha
SurjVal.v valp 2 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl.ha
SurjVal.v valp p ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl.ha
SurjVal.v valp p ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

hp: p = 2 p = 3

valp: SurjVal p


SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp (3 * 4) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp (3 * 4) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr.ha
SurjVal.v valp 3 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr.ha
SurjVal.v valp 3 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr.ha
SurjVal.v valp p ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr.ha
SurjVal.v valp p ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1

Goals accomplished! 🐙
lemma
v_rst_b2_of_small_char: ∀ {p : R} (valp : SurjVal p) (e : ValidModel R) (r s t : R), SurjVal.v valp (Model.b2 e.toModel) ofN 1SurjVal.v valp 12 ofN 1SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1
v_rst_b2_of_small_char
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.28902} → R[inst : IntegralDomain R] → Type ?u.28902
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.28911) → [inst : IntegralDomain R] → Type ?u.28911
ValidModel
R: Type u
R
) (
r: R
r
s: R
s
t: R
t
:
R: Type u
R
) (
h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1
h_b2
:
valp: SurjVal p
valp
.
v: {R : Type ?u.28922} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b2: {R : Type ?u.28934} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
1: ?m.28943
1
) (
h_p: SurjVal.v valp 12 ofN 1
h_p
:
valp: SurjVal p
valp
.
v: {R : Type ?u.28961} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
12: ?m.28966
12
ofN: ℕ∪∞
ofN
1: ?m.29029
1
) :
valp: SurjVal p
valp
.
v: {R : Type ?u.29036} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
rst_iso: {R : Type ?u.29040} → [inst : IntegralDomain R] → RRRValidModel RValidModel R
rst_iso
r: R
r
s: R
s
t: R
t
e).
b2: {R : Type ?u.29046} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
1: ?m.29053
1
:=
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (Model.rst_iso r s t e.toModel)) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (Model.rst_iso r s t e.toModel)) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 e.toModel + 12 * r) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 e.toModel + 12 * r) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (12 * r) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1

Goals accomplished! 🐙
section cubic def
Δcubic: {R : Type u} → [inst : IntegralDomain R] → R × R × RR
Δcubic
(
c: R × R × R
c
:
R: Type u
R
×
R: Type u
R
×
R: Type u
R
) :
R: Type u
R
:=
18: ?m.29296
18
*
c: R × R × R
c
.
1: {α : Type ?u.29306} → {β : Type ?u.29305} → α × βα
1
*
c: R × R × R
c
.
2: {α : Type ?u.29312} → {β : Type ?u.29311} → α × ββ
2
.
1: {α : Type ?u.29316} → {β : Type ?u.29315} → α × βα
1
*
c: R × R × R
c
.
2: {α : Type ?u.29320} → {β : Type ?u.29319} → α × ββ
2
.
2: {α : Type ?u.29324} → {β : Type ?u.29323} → α × ββ
2
-
4: ?m.29334
4
*
c: R × R × R
c
.
1: {α : Type ?u.29347} → {β : Type ?u.29346} → α × βα
1
^
3: ?m.29351
3
*
c: R × R × R
c
.
2: {α : Type ?u.29361} → {β : Type ?u.29360} → α × ββ
2
.
2: {α : Type ?u.29365} → {β : Type ?u.29364} → α × ββ
2
+
c: R × R × R
c
.
1: {α : Type ?u.29375} → {β : Type ?u.29374} → α × βα
1
^
2: ?m.29379
2
*
c: R × R × R
c
.
2: {α : Type ?u.29392} → {β : Type ?u.29391} → α × ββ
2
.
1: {α : Type ?u.29396} → {β : Type ?u.29395} → α × βα
1
^
2: ?m.29400
2
-
4: ?m.29413
4
*
c: R × R × R
c
.
2: {α : Type ?u.29426} → {β : Type ?u.29425} → α × ββ
2
.
1: {α : Type ?u.29430} → {β : Type ?u.29429} → α × βα
1
^
3: ?m.29434
3
-
27: ?m.29447
27
*
c: R × R × R
c
.
2: {α : Type ?u.29460} → {β : Type ?u.29459} → α × ββ
2
.
2: {α : Type ?u.29464} → {β : Type ?u.29463} → α × ββ
2
^
2: ?m.29468
2
def
model_to_cubic: {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.32385} → R[inst : IntegralDomain R] → Type ?u.32385
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.32394) → [inst : IntegralDomain R] → Type ?u.32394
ValidModel
R: Type u
R
) :
R: Type u
R
×
R: Type u
R
×
R: Type u
R
:= (evr.
sub_val: {R : Type ?u.32412} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e.
a2: {R : Type ?u.32430} → [inst : IntegralDomain R] → Model RR
a2
1: ?m.32436
1
, evr.
sub_val: {R : Type ?u.32450} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e.
a4: {R : Type ?u.32463} → [inst : IntegralDomain R] → Model RR
a4
2: ?m.32467
2
, evr.
sub_val: {R : Type ?u.32472} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e.
a6: {R : Type ?u.32485} → [inst : IntegralDomain R] → Model RR
a6
3: ?m.32489
3
) def
cubic_has_dinstinct_roots: {p : R} → EnatValRing pValidModel RProp
cubic_has_dinstinct_roots
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.32564} → R[inst : IntegralDomain R] → Type ?u.32564
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.32573) → [inst : IntegralDomain R] → Type ?u.32573
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= evr.
valtn: {R : Type ?u.32582} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.32589} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
Δcubic: {R : Type ?u.32596} → [inst : IntegralDomain R] → R × R × RR
Δcubic
(
model_to_cubic: {R : Type ?u.32599} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) =
0: ?m.32608
0
def
δmultiplicity: R × R × RR
δmultiplicity
(
c: R × R × R
c
:
R: Type u
R
×
R: Type u
R
×
R: Type u
R
) :
R: Type u
R
:=
3: ?m.32888
3
*
c: R × R × R
c
.
2: {α : Type ?u.32898} → {β : Type ?u.32897} → α × ββ
2
.
1: {α : Type ?u.32904} → {β : Type ?u.32903} → α × βα
1
-
c: R × R × R
c
.
1: {α : Type ?u.32911} → {β : Type ?u.32910} → α × βα
1
^
2: ?m.32915
2
def
cubic_has_double_root: {p : R} → EnatValRing pValidModel RProp
cubic_has_double_root
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.33482} → R[inst : IntegralDomain R] → Type ?u.33482
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.33491) → [inst : IntegralDomain R] → Type ?u.33491
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= evr.
valtn: {R : Type ?u.33500} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.33507} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
Δcubic: {R : Type ?u.33514} → [inst : IntegralDomain R] → R × R × RR
Δcubic
(
model_to_cubic: {R : Type ?u.33517} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) >
0: ?m.33526
0
evr.
valtn: {R : Type ?u.33780} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.33784} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
δmultiplicity: {R : Type ?u.33788} → [inst : IntegralDomain R] → R × R × RR
δmultiplicity
(
model_to_cubic: {R : Type ?u.33791} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) =
0: ?m.33796
0
def
cubic_has_triple_root: {p : R} → EnatValRing pValidModel RProp
cubic_has_triple_root
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.33830} → R[inst : IntegralDomain R] → Type ?u.33830
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.33839) → [inst : IntegralDomain R] → Type ?u.33839
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= evr.
valtn: {R : Type ?u.33848} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.33855} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
Δcubic: {R : Type ?u.33862} → [inst : IntegralDomain R] → R × R × RR
Δcubic
(
model_to_cubic: {R : Type ?u.33865} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) >
0: ?m.33874
0
evr.
valtn: {R : Type ?u.34128} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.34132} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
δmultiplicity: {R : Type ?u.34136} → [inst : IntegralDomain R] → R × R × RR
δmultiplicity
(
model_to_cubic: {R : Type ?u.34139} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) >
0: ?m.34144
0
def
move_cubic_double_root_to_origin_iso: {p : R} → EnatValRing pValidModel RValidModel R
move_cubic_double_root_to_origin_iso
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.34179} → R[inst : IntegralDomain R] → Type ?u.34179
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.34188) → [inst : IntegralDomain R] → Type ?u.34188
ValidModel
R: Type u
R
) :
ValidModel: (R : Type ?u.34192) → [inst : IntegralDomain R] → Type ?u.34192
ValidModel
R: Type u
R
:= let (
a2p: R
a2p
,
a4p2: R
a4p2
,
Warning: unused variable `a6p3` [linter.unusedVariables]
) :=
model_to_cubic: {R : Type ?u.34198} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e
rst_iso: {R : Type ?u.34255} → [inst : IntegralDomain R] → RRRValidModel RValidModel R
rst_iso
(
p: R
p
* (evr.
norm_repr: {R : Type ?u.34261} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(if evr.
residue_char: {R : Type ?u.34266} → {p : R} → [inst : IntegralDomain R] → EnatValRing p
residue_char
=
2: ?m.34271
2
then
a4p2: R
a4p2
else
a2p: R
a2p
*
a4p2: R
a4p2
)))
0: ?m.34474
0
0: ?m.34529
0
e def
cubic_double_root_is_zero: {p : R} → EnatValRing pValidModel RProp
cubic_double_root_is_zero
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.34865} → R[inst : IntegralDomain R] → Type ?u.34865
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.34874) → [inst : IntegralDomain R] → Type ?u.34874
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= let (
a2p: R
a2p
,
a4p2: R
a4p2
,
a6p3: R
a6p3
) :=
model_to_cubic: {R : Type ?u.34882} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e evr.
valtn: {R : Type ?u.34939} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.34943} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a2p: R
a2p
=
0: ?m.34951
0
evr.
valtn: {R : Type ?u.35201} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.35205} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a4p2: R
a4p2
>
0: ?m.35210
0
evr.
valtn: {R : Type ?u.35231} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.35235} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a6p3: R
a6p3
>
0: ?m.35240
0
lemma
Warning: declaration uses 'sorry'
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.35366} → R[inst : IntegralDomain R] → Type ?u.35366
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.35375) → [inst : IntegralDomain R] → Type ?u.35375
ValidModel
R: Type u
R
) :
cubic_has_double_root: {R : Type ?u.35380} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RProp
cubic_has_double_root
evr e
cubic_double_root_is_zero: {R : Type ?u.35393} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RProp
cubic_double_root_is_zero
evr (
move_cubic_double_root_to_origin_iso: {R : Type ?u.35400} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RValidModel R
move_cubic_double_root_to_origin_iso
evr e) :=
sorry: ?m.35413
sorry
def
move_cubic_triple_root_to_origin_iso: {p : R} → EnatValRing pValidModel RValidModel R
move_cubic_triple_root_to_origin_iso
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.35435} → R[inst : IntegralDomain R] → Type ?u.35435
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.35444) → [inst : IntegralDomain R] → Type ?u.35444
ValidModel
R: Type u
R
) :
ValidModel: (R : Type ?u.35448) → [inst : IntegralDomain R] → Type ?u.35448
ValidModel
R: Type u
R
:= let (
a2p: R
a2p
,
Warning: unused variable `a4p2` [linter.unusedVariables]
,
a6p3: R
a6p3
) :=
model_to_cubic: {R : Type ?u.35454} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e
rst_iso: {R : Type ?u.35511} → [inst : IntegralDomain R] → RRRValidModel RValidModel R
rst_iso
(
p: R
p
* (evr.
norm_repr: {R : Type ?u.35517} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(if evr.
residue_char: {R : Type ?u.35522} → {p : R} → [inst : IntegralDomain R] → EnatValRing p
residue_char
=
2: ?m.35527
2
then -
a2p: R
a2p
else -
a6p3: R
a6p3
)))
0: ?m.35707
0
0: ?m.35762
0
e def
cubic_triple_root_is_zero: {p : R} → EnatValRing pValidModel RProp
cubic_triple_root_is_zero
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.36076} → R[inst : IntegralDomain R] → Type ?u.36076
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.36085) → [inst : IntegralDomain R] → Type ?u.36085
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= let (
a2p: R
a2p
,
a4p2: R
a4p2
,
a6p3: R
a6p3
) :=
model_to_cubic: {R : Type ?u.36093} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e evr.
valtn: {R : Type ?u.36150} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.36154} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a2p: R
a2p
>
0: ?m.36162
0
evr.
valtn: {R : Type ?u.36416} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.36420} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a4p2: R
a4p2
>
0: ?m.36425
0
evr.
valtn: {R : Type ?u.36443} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.36447} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a6p3: R
a6p3
>
0: ?m.36452
0
lemma
Warning: declaration uses 'sorry'
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.36578} → R[inst : IntegralDomain R] → Type ?u.36578
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.36587) → [inst : IntegralDomain R] → Type ?u.36587
ValidModel
R: Type u
R
) :
cubic_has_triple_root: {R : Type ?u.36592} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RProp
cubic_has_triple_root
evr e
cubic_triple_root_is_zero: {R : Type ?u.36605} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RProp
cubic_triple_root_is_zero
evr (
move_cubic_triple_root_to_origin_iso: {R : Type ?u.36612} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RValidModel R
move_cubic_triple_root_to_origin_iso
evr e) :=
sorry: ?m.36625
sorry
end cubic end ValidModel